Classical Mechanics

1. Gravitation
   1. Newton’s Law of Universal Gravitation
      1. Definition and Historical Context
         1. Isaac Newton's formulation of the law
         2. Historical experiments supporting the law
      2. Mathematical Representation
         1. Universal gravitational constant (G)
         2. Formula: F = G * (m1 * m2) / r^2
      3. Applications
         1. Calculation of gravitational force between two masses
         2. Weight as a specific case of gravitational force
         3. Gravitational interactions in everyday life
   2. Gravitational Fields and Potential
      1. Gravitational Field
         1. Definition and concept of gravitational field strength
         2. Representation of gravitational fields with field lines
         3. Calculations involving gravitational field strength
      2. Gravitational Potential Energy
         1. Definition and derivation of gravitational potential energy
         2. Relation to work done against a gravitational field
         3. Negative potential energy and conventions
      3. Gravitational Potential
         1. Definition and difference from gravitational potential energy
         2. Equipotential surfaces and their properties
         3. Calculations involving gravitational potential
   3. Motion of Planets and Satellites
      1. Kepler’s Laws of Planetary Motion
         1. First Law (Law of Orbits): Planets move in elliptical orbits
         2. Second Law (Law of Areas): Equal areas in equal times
         3. Third Law (Law of Periods): Relationship with the semi-major axis of orbits
      2. Orbits
         1. Types of orbits: circular, elliptical, parabolic, hyperbolic
         2. Orbital speed and period
         3. The influence of gravitational perturbations on orbits
      3. Satellites
         1. Definition and examples of natural and artificial satellites
         2. Geostationary versus polar orbits
         3. The role of gravity in maintaining satellite orbits
      4. Escape Velocity
         1. Definition and derivation of escape velocity
         2. Factors affecting escape velocity
         3. Applications of escape velocity in space exploration
   4. Tidal Forces and Effects
      1. Definition of tidal forces
      2. Origin and implications of tides on Earth
         1. Spring and neap tides
         2. Tidal locking and its effects (e.g., Moon's synchronous rotation)
      3. Tidal friction and its role in slowing Earth's rotation
   5. Gravitational Waves
      1. Predicted by General Relativity
      2. Definition and characteristics of gravitational waves
      3. Methods of detection (e.g., LIGO)
      4. Implications for astrophysics and cosmology
   6. General Relativity Concepts Relevant to Gravitation
      1. Einstein's theory of General Relativity and its modification of classical gravity
      2. Concept of spacetime curvature
      3. Tests of General Relativity related to gravitation (e.g., gravitational lensing, perihelion precession of Mercury)
   7. Gravitational Anomalies and Phenomena
      1. Gravitational lensing
         1. Definition and effects on light propagation
         2. Applications in observing distant astronomical objects
      2. Gravitational time dilation
         1. Concept and examples
         2. Confirmations through experiments and observations
      3. Black holes
         1. Prediction from theory and observational evidence
         2. Event horizon and singularity concepts